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Suppose we have two objects sitting on two side of a lever, and the lever also has a mass, and those objects have masses. Then how we can balance $\sum τ$?

This is what I have done:

$$\begin{multline}M_\text{heavier}\times g\times D_\text{from center to heavier} - M_\text{lighter}\times g\times D_\text{from center to lighter} \\ - \text{torque caused by mass of lever}\end{multline}$$

where $D= \text{distance from center}$

I don't know to to include torque cased by mass of lever

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4  
Lever with mass $m$ = Massless lever + object with mass $m$ located at center of mass of the original lever. –  leongz Dec 18 '12 at 7:43
1  
You need to know the distance between the level center of gravity and the fulcrum. Then as @leongz said, apply the level mass there, –  ja72 Dec 18 '12 at 10:47
    
If the lever has a uniform density, you could integrate to find it's moment of inertia. Then the torque can be calculated from there. –  Kitchi Dec 25 '12 at 16:14

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